Due to the increased demands for improved receiver performance, many advanced receivers use zero forcing (ZF) block linear equalizers and minimum mean square error (MMSE) equalizers.
In both these approaches, the received signal is typically modeled per Equation 1.r=Hd+n  Equation 1
r is the received vector, comprising samples of the received signal. H is the channel response matrix. d is the data vector. In spread spectrum systems, such as code division multiple access (CDMA) systems, d is the spread data vector. In CDMA systems, data for each individual code is produced by despreading the estimated data vector d with that code. n is the noise vector.
In a ZF block linear equalizer, the data vector is estimated, such as per Equation 2d=(H)−1r  Equation 2
(·)H is the complex conjugate transpose (or Hermetian) operation. In a MMSE block linear equalizer, the data vector is estimated, such as per Equation 3.d=(HHH+σ2I)−1r  Equation 3
In wireless channels experiencing multipath propagation, to accurately detect the data using these approaches requires that an infinite number of received samples be used. One approach to reduce the complexity is a sliding window approach. In the sliding window approach, a predetermined window of received samples and channel responses are used in the data detection. After the initial detection, the window is slid down to a next window of samples. This process continues until the communication ceases.
By not using an infinite number of samples, an error is introduced into the data detection. The error is most prominent at the beginning and end of the window, where the effectively truncated portions of the infinite sequence have the largest impact. One approach to reduce these errors is to use a large window size and truncate the results at the beginning and the end of the window. The truncated portions of the window are determined in previous and subsequent windows. This approach has considerable complexity. The large window size leads to large dimensions on the matrices and vectors used in the data estimation. Additionally, this approach is not computationally efficient by detection data at the beginning and at the ends of the window and then discarding that data.
Accordingly, it is desirable to have alternate approaches to data detection.